Hello!!
Suppose that $R$ is a commutative ring and $(x,y)$ is an ideal.
We have that $(x,y)^2=(x,y)(x,y)=\{ij \mid i\in (x,y) , j\in (x,y)\}=\{x^2, xy, yx, y^2\}=\{x^2, xy, y^2\}$.
Is the ideal $(x^2,xy, y^2)$ equal to the set $\{x^2, xy , y^2\}$ ? Or is it maybe $\{x^2, xy , y^2\}\subseteq (x^2, xy , y^2)$ ?